MC21 / CTF and VERA Multiphysics Solutions to VERA Core Physics Benchmark Progression Problems 6 and 7

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1 MC21 / CTF and VERA Multiphysics Solutions to VERA Core Physics Benchmark Progression Problems 6 and 7 Daniel J. Kelly III a,*, Ann E. Kelly a, Brian N. Aviles a Andrew T. Godfrey b, Robert K. Salko b, Benjamin S. Collins b a Naval Nuclear Laboratory, Knolls Atomic Power Laboratory, Schenectady, NY 12301, USA *daniel.kelly@unnpp.gov b Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN, 37831, USA Abstract The continuous energy Monte Carlo neutron transport code, MC21, was coupled to the CTF subchannel thermal-hydraulics code using a combination of CASL tools and in-house Python scripts. An MC21/CTF solution for VERA Core Physics Benchmark Progression Problem 6 demonstrated excellent agreement with MC21/COBRA-IE and VERA solutions. The MC21/CTF solution for VERA Core Physics Benchmark Progression Problem 7, Watts Bar Unit 1 at beginning of cycle (BOC) hot full power (HFP) equilibrium xenon conditions, is the first published coupled Monte Carlo neutronics / subchannel T-H solution for this problem. MC21/CTF predicted a critical boron concentration of ppm, yielding a critical eigenvalue of ± 6.8E-6 (95% CI). Excellent agreement with a VERA solution of Problem 7 was also demonstrated for integral and local power and temperature parameters. I. INTRODUCTION Monte Carlo reactor physics codes coupled with subchannel thermal-hydraulics (T-H) codes are becoming more common for the solution of large-scale nuclear reactor problems [1, 2]. These complement the growing number of coupled deterministic transport reactor physics / subchannel T-H codes applied to similar systems-level reactor problems. This paper describes the coupling of the continuous energy Monte Carlo code, MC21 [3], to the subchannel T-H code, CTF [4], which is part of the Consortium for Advanced Simulation of Light Water Reactor s (CASL) Virtual Environment for Reactor Applications (VERA) code system [5, 6]. MC21/CTF solutions for CASL VERA Core Physics Benchmark Progression Problems 6 and 7 [7] are presented and compared to VERA solutions (MPACT coupled to CTF) of the same benchmark problems. II. MC21 / CTF COUPLING Previous work reported the coupling of MC21 and COBRA-IE [8] for the analysis of a hot-full-power (HFP) Pressurized Water Reactor (PWR) assembly [9]. COBRA- IE and CTF share a common COBRA ancestor but have been developed separately. Because CTF is the subchannel T-H code in VERA, it is desirable to couple MC21 and CTF to fully separate differences between neutronics and T-H effects. In this work, MC21 is coupled to CTF using a combination of modules from VERA and in-house Python scripts, as shown in Fig. 1 through Fig. 3 and described below. Input processing for VERA is performed using the VERAIn common input parser and VERA processing tools [10] (Fig. 1) to generate CTF model input and geometry information needed to map results between MC21 and CTF. CTF input is generated for the complete model using that VERA input file. Although this section describes the Problem 7 benchmark, a ¼-core model of Watts Bar Unit 1, the Problem 6 benchmark model with a single assembly (and single CTF input / output file) was also run using the same process with different input arguments. The MC21 model input file is processed with the Physics Unified Modeling and Analysis (PUMA) system, which generates all necessary input files for MC21 execution (Fig. 2). PUMA and MC21 are part of the Common Monte Carlo Design Tool (CMCDT) project at the Naval Nuclear Laboratory [3,11]. MC21 is executed initially with isothermal T-H conditions. With MC21 and CTF model initialization complete, a converged mutually-consistent neutronics and T-H solution is performed via Picard iteration (Fig. 3). First, the in-house mc21_to_ctf.py script combines geometry information from the CTF model with fission tallies and additional job information from MC21 to compute relative linear heat rate distributions for each assembly. The process utilizes the CTF HDF5 pdeck.h5 file and the power distribution information is written to the pin_powers data set in that file in the correct assembly locations. Second, CTF is then executed using the multistate_cobra external driver program [12] and the newly generated pdeck.h5 file containing the MC21 power distributions, as well as the CTF model generated from the VERAin file. Third, subchannel temperatures and densities, and fuel rod volumeaverage temperatures are collected from the CTF HDF5 output by the in-house ctf_to_mc21.py script and translated back to the proper MC21 regions. These temperatures and densities are saved in an MC21 HDF5 file that will be imported in the next execution of MC21. Fourth, MC21 is executed with updated T-H conditions. The Picard iteration in Fig. 3 is repeated until convergence is achieved.

2 Fig. 1. VERAIn / CTF Pre-Processing Flowchart (Blue = VERA codes and files) Fig. 3. MC21 / CTF Picard Iteration Flowchart (Blue = VERA codes and files, Green = CMCDT codes and files, Magenta = in-house scripts), dashed lines = files generated in preprocessing steps III. MODEL DESCRIPTION Fig. 2. MC21 Pre-Processing and Initial Isothermal Job (Green = CMCDT codes and files) The MC21 model was generated using the PUMA model builder which is part of the CMCDT project [11]. PUMA input is based on a Java input deck which easily enables the user to build complicated geometries using built-in methods in addition to the many features of the Java programming language. Specifications of the VERA benchmark problems are taken from [7]. New to this work is the restructuring of the PUMA model to more easily facilitate the construction of MC21 models based on the VERA common input file [10]. Building MC21 models with this format simplifies model construction as well as enhances model quality assurance by enabling direct model input comparisons between the corresponding VERA and PUMA/MC21 models. For PUMA to support this type of format, a separate Java class (VERA-Util) was written to handle model construction. At this stage of development, the various VERA input cards such as cell, lattice, axial, and assm_map (to name a few) are reformatted to work within the PUMA framework. Ideally, a PUMA translator

3 would read these cards directly. For both VERA Benchmark Problems 6 and 7, the 2D lattices were constructed using octant-symmetry. The corresponding VERA input files are available from CASL. An example extracted from the PUMA input file to construct a pin cell and corresponding fuel lattice is shown below. TFB Subchannel Figure f1 = VERAUtil.makePinCell("F1", " / u21 he zirc4"); This line describes the various concentric rings as well as the materials to be assigned to each region. The portion of code that specifies input required to construct a fuel lattice in PUMA using octant symmetry with the VERAUtil class is show below. Figure[] fig26 = { g4, f1, f1, f1, f1, f1, g4, f1, f1, g4, f1, f1, f1, f1, f1, f1, f1, f1, f1, f1, g4, g4, f1, f1, g4, f1, f1, f1, f1, f1, f1, f1, f1, f1, f1, f1, f1, f1, f1, f1, f1, f1, f1, f1, f1}; Overlay lat26= VERAUtil.makeLattice("LAT26", fig26) In a standard MC21 PUMA model, each unit cell is constructed from five regions consisting of two squares (the outer square is either spacer grid material or coolant and the inner square is subchannel coolant) and three concentric circles (clad, gap, and fuel). For a thermal-hydraulic feedback (TFB) model, 11 regions are required since the grid and coolant regions are each subdivided into quadrants (Fig. 4). In addition, the TFB case requires that the respective quadrant from one pin cell share a common attribute with the adjoining quadrants in the neighboring pin cell so that a compatible sub-channel is defined to interface with the CTF model (Fig. 5). Fuel pins are specified as a complete pin and a separate attribute is assigned to these regions. Standard Model TFB Model Fig. 4. MC21 PUMA Description of Pin Cell Geometry Fig. 5. MC21 PUMA Description of Subchannel Geometry The attribute mentioned above is a powerful feature of PUMA where specific properties, called attributes, can be assigned to geometric figures during model creation such that a specific set of figures can be grouped together for the purpose of edits and/or material assignments. As part of the internal temperature feedback capabilities of MC21 [3], specific attributes called source and sink are used to specify power generating regions (sources) and coolant regions (sinks). In the MC21 input files, specific input is given for these two attributes in addition to the standard region id and material id. In addition, the temperature feedback capability of MC21 specifies a unique file format whereby the user can specify the temperature of the sources (i.e., fuel pins) and both the temperature and density of the sinks (i.e., coolant regions) to achieve the effects of temperature feedback on MC21 material number densities and cross sections. These input files and features of MC21 and PUMA allow MC21 to be coupled to external T-H codes such as CTF. IV. RESULTS 1. VERA Core Physics Benchmark Problem 6 VERA Core Physics Benchmark Problem 6 is a PWR fuel assembly at HFP conditions [7]. Problem 6 was simulated without guide tube heating using MC21/CTF to demonstrate that coupling of MC21 and CTF using the process described in Section II was working properly. MC21/CTF results are compared with updated MC21/COBRA-IE and VERA solutions from [9]. The MC21 and CTF assembly geometry is described in [7, 9]. MC21 uses cross sections from ENDF/B-VII.1, with nonwater material cross sections ranging from 500 K to 1600 K in 50 K increments up to 900 K and 100 K increments thereafter, and water cross sections ranging from 500 K to 650 K at 10 K intervals. MPACT employs a 51 energy group cross section library based on ENDF/B-VII.1 data with subgroup parameters to capture self-shielding effects. Nine coupled iterations were simulated to converge MC21 and CTF. Fig. 6 presents the MC21 eigenvalue trajectory during the nine data exchanges. The number of active neutron histories for each data exchange is shown on

4 MC21 Eigenvalue Active Histories (Billion Neutrons) M&C International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, the right axis and increases from 200 million histories at the first data exchange to 2 billion histories for data exchanges 5 through 9 (200 active generations of 10 million neutrons per generation preceded by 50 discarded generations). Two billion histories were adequate to reduce uncertainties in local pin power < 0.7% [9]. The MC21 eigenvalue is converged at data exchange 5 when the two billion active neutron history value is reached MC21 Eigenvalue 1.0 Fig. 7. CTF Convergence Metrics for Subchannel Coolant Temperature during MC21/CTF Data Exchanges Active Neutron Histories MC21/CTF Data Exchange Index Fig. 6. MC21 Eigenvalue and Number of Active Neutron Histories during MC21/CTF Data Exchanges Local subchannel coolant temperature, average fuel rod temperature, and pin linear heat rate convergence metrics, as measured by the L 2 and L norms with respect to their respective final (exchange index 9) distributions, are presented in Fig. 7 Fig. 9. As was done in [9], the L 2 norm for coolant temperature was normalized by the square root of the number of subchannel regions (4410), and the L 2 norms for fuel temperature and pin linear heat rate were normalized by the square root of the number of fuel regions (3528). These norms also indicate that the coupled MC21/CTF solution is converged at data exchange 5, as local coolant temperatures are within 0.02 C, local fuel temperatures are within 3 C, and local pin linear heat rates are within 2 W/cm of their final data exchange values, respectively. Table I presents calculated eigenvalues for the three code systems. MC21/CTF and MC21/COBRA-IE produce statistically-equivalent eigenvalues. Table I. Calculated Eigenvalues for CASL P6 ¼-Assembly Code System Eigenvalue (95% CI) Difference (pcm) MC21/COBRA-IE (2.6E-05) Reference MC21/CTF (2.6E-05) 0 MPACT/CTF Fig. 8. CTF Convergence Metrics for Fuel Temperature during MC21/CTF Data Exchanges Fig. 9. CTF Convergence Metrics for Pin Linear Heat Rate during MC21/CTF Data Exchanges Fig. 10 presents axially-integrated ¼-assembly normalized pin fission rates, and Fig. 11 presents subchannel exit coolant temperatures for all three code

5 systems. MC21/CTF produces results nearly identical to MC21/COBRA-IE and consistent with VERA, indicating excellent agreement between MC21 and MPACT power distributions and COBRA-IE and CTF T-H solutions for this ¼-assembly HFP benchmark problem. Focusing on MC21/CTF comparisons with VERA, the maximum differences in axially-integrated pin power are -0.19% in pin (9,10) and +0.17% in pin (13,13) with a root mean square (RMS) difference of 0.09%. Subchannel exit coolant temperatures agree within ±0.1 C with an RMS difference of 0.02 C MC21/CTF MC21/COBRA-IE VERA Color Key Fig. 10. Axially-Integrated ¼-Assembly Normalized Pin Fission Rate Comparison, VERA Problem 6 libraries for MC21 and MPACT for Problem 7 are identical to Problem 6, as described in Section IV.1. In this analysis, all central instrument tubes were replaced with guide tubes to enable ¼-core symmetry. Instrument tubes will be reinstated when future comparisons with flux maps are performed. A reactivity sensitivity study of replacing instrument tubes with guide tubes was performed with VERA, indicating that guide tubes are worth ~4 ppm of boron (~40 pcm). MPACT was executed using the 2D/1D technique with transport-corrected P 0 2D MOC in the radial planes and SP 3 in the axial direction. Temperature and density changes are monitored to determine if the subgroup calculation needs to be re-executed to obtain new shielding parameters for cross section generation Fig. 11. Subchannel Exit Coolant Temperature Comparison, VERA Problem 6 2. VERA Core Physics Benchmark Problem 7 MC21/CTF (C) MC21/COBRA-IE (C) VERA (C) Guide Tube Location VERA Core Physics Benchmark Problem 7 represents Watts Bar Nuclear Unit 1 at Beginning-of-Cycle (BOC), HFP, equilibrium xenon conditions [7], with different fuel enrichments of 2.11% (red), 2.619% (green), and 3.10% (blue), respectively, as shown in Fig. 12. The cross section Fig. 12. PUMA Visualization of ¼-Core MC21 Model for VERA Problem 7 A. MC21/CTF Running Strategy MC21 was executed using the critical boron search feature of MC21 at equilibrium xenon conditions with full thermal-hydraulic feedback using fuel and coolant temperatures and coolant densities from CTF. Table II describes the running strategy and results for MC21/CTF during the five Picard iterations. The goal was to compute critical boron such that MC21 s eigenvalue was within ±10 pcm of unity. Critical boron searches were performed in iterations 2 and 3. The critical boron concentration search range for MC21 was set from 700 ppm to 900 ppm, and MC21 automatically performs partial spatial solutions until the eigenvalue is within a user-specified tolerance (±10 pcm in this study), at which time MC21 performs a full spatial solution. Equilibrium xenon was updated every five

6 % Regions M&C International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, generations (user specified). Note that in iteration 4, as the number of active histories increased, the more tightlyconverged power solution affected the temperature distributions and caused the calculated eigenvalue to stray outside the ±10 pcm target set by the earlier critical boron searches. Based on MC21 s estimate of boron sensitivity from these earlier iterations (~10.3 pcm/ppm), boron concentration was re-adjusted prior to iteration 5. Iteration 5 was then executed as a restart from the iteration 4 solution with 30 billion active neutron histories (7500 active generations of 4 million neutrons / generation, 50 discarded generations) with the goal of driving the uncertainty on local pin power to ~2%, based on [11]. No variance reduction techniques were employed in this study. For the 5 th Picard iteration, MC21 required 164 wall clock hours (6.8 days) using 32 nodes containing two 16-core Intel Xeon E5-2683v4 2.1GHz (Broadwell) processors (1024 total cores). VERA execution took 57 minutes using 464 cores on Idaho National Laboratory s Falcon computer (Intel Xeon E5-2680v3 2.5GHz processors). Table II. MC21/CTF Running Strategy Picard Iter Actions Fixed Boron, Isothermal, eqxe Boron Search, T/H Feedback, eqxe Boron Search, T/H Feedback, eqxe Fixed Boron, T/H Feedback, eqxe Fixed Boron, T/H Feedback, eqxe Boron (ppm) Active Histories (generation size) 50 million (500,000) 100 million (1 million) 100 million (1 million) 500 million (1 million) 30 billion (4 million) B. Select MC21/CTF and VERA Comparisons k calc (95% CI) (1.8E-4) (1.2E-4) (1.0E-4) (4.8E-5) (6.8E-6) From Table II, a final critical boron concentration of ppm resulted in an MC21 eigenvalue of ± 6.8E-6 (95% CI). VERA computes a critical boron concentration of ppm for the target eigenvalue of 1.0. Both codes are in excellent agreement for this parameter. Fig. 13 presents the relative uncertainty in MC21 relative power density (RPD) after Iteration 5 for all 628,572 mesh tally regions in the ¼-core model in 0.25% resolution bins. At 30 billion active histories, the majority of local power regions (52.9%) have relative uncertainties less than 0.5%, 94.4% of all regions have relative uncertainties less than 1.0%, and 99.9% of all regions have relative uncertainties less than 2% (the target for this study). The average relative uncertainty is 0.56%. Considering only local power regions with a relative power greater than 1.0, the maximum relative uncertainty is 1.1%, and the average uncertainty for these regions is 0.43%. As expected, the regions with the highest local power uncertainties occur in the top and bottom few axial planes, primarily near the core periphery. This is demonstrated in Fig. 14 and Fig. 15, which shows regions with relative uncertainties >1% and >2%, respectively, from a visual perspective at the bottom corner of the core. The maximum relative uncertainty is 3.59% in the first axial plane of pin (17,17) in Assembly B-13, and the minimum relative uncertainty of 0.32% occurs at axial plane 18 ( cm to cm) in pin (6,6) in Assembly D-10. The very few regions with uncertainties >2% are confined to the outer few pins in the two top and bottom axial planes (Fig. 15). Also note from Fig. 14 that the core periphery regions with smaller volumes in planes containing spacer grids also have slightly higher uncertainties than surrounding regions. 100% 90% 80% 70% 60% 50% 40% 30% 20% 52.9% 85.2% 32.3% 98.1% 99.4% 99.7% 99.9% 100.0% 94.4% % Regions in Local Uncertainty Bin % Regions (Cumulative) 9.2% 10% 3.7% 0.0% 1.3% 0.4% 0.2% 0.1% << 0.1% 0% from to % Uncertainty in Local Power (95% CI) Fig. 13. Distribution of MC21 Relative Uncertainty in RPD for VERA Problem 7, 30 Billion Neutrons Fig. 16 presents MC21 axially-integrated relative pin power. The MC21 maximum relative pin power of occurs in pin (4,5) in Assembly D-12. VERA predicts the maximum power in the same pin with a value of , a difference of 0.09%. MC21/CTF predicts the pin with the smallest relative power to be for pin (17,17) in Assembly C-14. VERA predicts a minimum pin relative power value of in the same pin, a -0.7% difference. Fig. 17 presents a 3D view of the relative pin power distribution from MC21/CTF. Maximum local power peaking on this tally mesh (pin resolved, 49 axial elevations) is with a relative uncertainty of 0.34%, occurring at axial plane 18 ( cm to cm) in pin (5,4) in Assembly D-12. For VERA, the maximum local power peaking value of occurs in the same pin one axial elevation higher ( cm to cm), a difference of 0.08%. This agreement is well within MC21 s local relative pin power uncertainty at both axial elevations,

7 as shown in the axial relative pin LHR comparison for this pin, presented in Fig. 18. Fig. 16. MC21 Axially-Integrated Relative Pin Power Distribution. Minimum = , Maximum = Fig. 14. Distribution of MC21 Relative Uncertainties in RPD > 1%, VERA Problem 7, 30 Billion Neutrons Fig. 15. Distribution of MC21 Relative Uncertainties in RPD > 2%, VERA Problem 7, 30 Billion Neutrons Fig. 17. MC21 3D Relative Pin Power Distribution, VERA Problem 7

8 Relative Power (-) % Difference: VERA vs. MC21/CTF Relative Pin Linear Heat Rate M&C International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Axial Height (cm) Fig. 18. Axial Relative LHR for Pin (5,4) in Assembly D- 12, MC21/CTF versus VERA, VERA Problem 7 An octant view of CTF coolant temperatures from MC21/CTF is presented in Fig. 19 showing subchannel T-H fidelity within the core region. axial relative power is 0.25%. Axial offsets for MC21/CTF and VERA are % and %, respectively. Fig. 22 presents assembly-averaged exit temperatures estimated by mass flow weighting the subchannel coolant temperatures in the top axial plane. Assembly exit coolant temperatures agree within -0.2/+0.2 C with an RMS difference of 0.13 C. These comparisons indicate that MC21/CTF and VERA solutions agree for integral assembly-averaged and radiallyaveraged quantities. MC21/CTF: Assembly D-12, pin (5,4) VERA: Assembly D-12, pin (5,4) H G F E D C B A MC21/CTF VERA -0.02% 0.24% 0.04% 0.26% 0.02% 0.15% -0.32% -0.09% % diff (VERA vs MC21/CTF) % 0.10% 0.34% 0.13% 0.29% -0.01% 0.02% -0.11% Color Key % 0.37% 0.15% 0.36% 0.10% 0.13% -0.33% -0.17% % 0.16% 0.35% 0.10% 0.23% -0.18% -0.11% -0.21% % 0.31% 0.05% 0.20% 0.00% -0.12% -0.21% % -0.08% 0.05% -0.26% -0.17% -0.31% -0.24% % -0.06% -0.46% -0.22% -0.31% -0.29% % -0.19% -0.27% -0.47% Fig. 20. Axially-Integrated Assembly Relative Power, MC21/CTF and VERA, Problem Axial Offset: MC21/CTF = % VERA = % 3% 1.3 2% 1.0 1% 0.8 0% MC21/CTF VERA % Difference: VERA vs. MC21/CTF -1% -2% Fig D Octant View of CTF Subchannel Temperature Distribution for MC21/CTF, VERA Problem 7 Fig. 20 presents axially-integrated assembly relative power for MC21/CTF and VERA. Assembly powers agree within -0.47%/+0.37%, with an RMS difference of 0.22%. Core-average axial power shape comparisons are presented in Fig. 21, again showing excellent agreement between codes. The poorer MC21 statistics in the top axial plane affects the difference in this low power core region. The RMS difference between VERA and MC21/CTF for the 0.0-3% Axial Height (cm) Fig. 21. Core Relative Axial Power and Axial Offset, MC21/CTF and VERA, Problem 7

9 H G F E D C B A MC21/CTF (C) VERA (C) Difference (C): VERA MC21/CTF Color Key Fig. 22. Assembly-Averaged Exit Coolant Temperature (C), MC21/CTF and VERA, Problem 7 Investigating local thermal-hydraulics quantities also demonstrates a high level of agreement between MC21/CTF and VERA. Fig. 23 is a 2D ¼-core map showing differences (VERA MC21/CTF) in subchannel exit coolant temperatures. All subchannel exit temperatures agree within -0.25C/+0.27C, and a majority (57%) of subchannels agree within ±0.1 C. Assembly F-14 (2.11% enrichment w/o poison) is the assembly in which VERA computes consistently lower exit coolant temperatures, and Assembly G-10 (2.619% enrichment with 24 Pyrex burnable absorber pins) is the assembly in which VERA predicts the highest subchannel exit temperatures compared to MC21/CTF. There is a checkerboard behavior in the differences between MC21/CTF and VERA for the 2.11% enriched assemblies with no poison pins and the 2.619% enriched assemblies with Pyrex absorber pins. A similar trend was seen in local power comparisons between VERA and the KENO Monte Carlo code for VERA Problem 5 (Watts Bar Unit 1 at hot zero power conditions). At this top axial level, the mean difference between VERA and MC21/CTF is 0.03 C with an RMS difference of 0.13 C. The RMS difference between VERA and MC21/CTF for all subchannel coolant temperature regions in the 3D ¼-core model is 0.08 C. Fig. 23. Difference in Subchannel Exit Coolant Temperature (C), (VERA MC21/CTF), VERA Problem 7 Fig. 24 presents a similar temperature difference plot, this time showing differences in local volume-averaged fuel pin temperatures at the axial plane with the maximum fuel temperature (axial plane 19 between cm and cm). Agreement at this plane is -8.6C/+7.3C, with 59% of pin fuel temperatures agreeing within ±2 C. The mean difference between VERA and MC21/CTF at this axial level is 0.20 C with an RMS difference of 2.1 C. Consistent with the exit coolant temperature map, Assembly F-14 is the assembly with the largest VERA versus MC21/CTF differences. Maximum volume-averaged fuel pin temperature is predicted by MC21/CTF to be C at pin (5,6) in Assembly D-12. Again, the checkerboard pattern in fuel temperatures between MC21 and MPACT in the 2.11% and 2.6 enriched assemblies is present in the fuel temperatures because of the differences in power distributions. There is also an observable octant tilt resulting from the non-symmetric MC21 solution with only 30 billion neutron histories (also evident in Fig. 20). The RMS difference between VERA and MC21/CTF for all fuel pin volume-average temperature regions in the 3D ¼-core model is 1.8 C.

10 project, and ORNL research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR REFERENCES Fig. 24. Difference in Volume-Averaged Fuel Pin Temperature (C) at Axial Plane 19, (VERA MC21/CTF), VERA Problem 7 V. CONCLUSIONS The continuous energy Monte Carlo neutron transport code, MC21, was coupled to the CTF subchannel thermalhydraulics code using a combination of CASL tools and inhouse Python scripts. MC21/CTF solutions for VERA Core Physics Benchmark Progression Problem 6 demonstrated excellent agreement with MC21/COBRA-IE and VERA solutions to the same benchmark problem. The MC21/CTF solution for VERA Core Physics Benchmark Progression Problem 7, Watts Bar Unit 1 at HFP equilibrium xenon conditions, represents the first published coupled Monte Carlo neutronics / subchannel T-H solution for this benchmark. MC21/CTF predicts a critical boron concentration of ppm, yielding a critical eigenvalue of ± 6.8E-6 (95% CI). Excellent agreement with a VERA solution of Problem 7 was demonstrated for estimated critical boron, assembly-level powers, axial power distribution, axial offset, and assembly exit temperatures. Comparisons of local pin and subchannel quantities also showed excellent agreement. ACKNOWLEDGMENTS The Naval Nuclear Laboratory authors would like to thank the MC21 and PUMA development teams for their support during this research. Work for the Oak Ridge National Laboratory authors was funded by the DOE-sponsored Consortium for Advanced Simulation of Light Water Reactors (CASL) 1. D. KELLY III, et al., Analysis of Select BEAVRS PWR Benchmark Cycle 1 Results using MC21 and OpenMC, Proc. PHYSOR 2014, Kyoto, Japan, September 28 October 3, 2014, American Nuclear Society (2014) (CD-ROM). 2. N. GUILLIARD, et al., Analysis of Large Core Neutronics by the Monte Carlo Method Coupled with Thermal Hydraulics, Proc. PHYSOR 2016, Sun Valley, Idaho, May 1 5, 2016, American Nuclear Society (2016) (CD-ROM). 3. D. GRIESHEIMER, et al., MC21 v.6.0 A Continuous-Energy Monte Carlo Particle Transport Code with Integrated Reactor Feedback Capabilities, Annals of Nuclear Energy, 82, (2015). 4. R. SALKO and M. AVRAMOVA, CTF Theory Manual, Reactor Dynamics and Fuel Management Group, Pennsylvania State University, M. SIEGER, VERA 3.3 Release Notes, CASL Technical Report: CASL-U , B. KOCHUNAS et al., VERA Core Simulator Methodology for PWR Cycle Depletion, CASL Technical Report: CASL-U , A. GODFREY, VERA Core Physics Benchmark Progression Problem Specifications, Revision 4, CASL Technical Report: CASL-U , D. AUMILLER, et al., COBRA-IE: A New Subchannel Analysis Code, Proc. NURETH-16, Chicago, Illinois, August 30 September 4, 2015, American Nuclear Society (2015) (CD-ROM). 9. B. AVILES, et al., Coupled MC21 and COBRA-IE Solution to VERA Core Physics Benchmark Problem #6, Proc. PHYSOR 2016, Sun Valley, Idaho, May 1 5, 2016, American Nuclear Society (2016) (CD-ROM). 10. S. PALMTAG and A. GODFREY, VERA Common Input User Manual, CASL Technical Report: CASL-U , D. KELLY III, et al., MC21 Monte Carlo Analysis of the Hoogenboom-Martin Full-Core PWR Benchmark Problem, Proc. PHYSOR 2010, Pittsburgh, Pennsylvania, May 9 May 14, 2010, American Nuclear Society (2010) (CD-ROM). 12. R. SALKO, Development of CTF Capability for Modeling Reactor Operating Cycles with Crud Growth, CASL Technical Report: CASL-U , 2014.J. GLEASON, Format for a Report, ANS-2008, American Nuclear Society (2008).